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equal to (1 - Cr) previously defined). The boxed-in elements
indicate our choices for "optimal" n/e separation points in order
of decreasing electron detection efficiency.
Six PHS classes were selected and are summarized in Table
11-I-3. A test of the analysis procedure is how invariant the
cross sections are to PHS class. Over the six classes the cross
sections were usually found to vary less than 4% absolute while
the detection efficiency varied by over 20% from the different
PHS cuts made.
TRACKING AND CODES
The first task in analyzing a hodoscope system is to assign
a unique slat to every event in each hodoscope. The backup coarse
hodoscope on the p-8 slats proved valuable in analyzing multiple
slat events. For example, in an event consisting of a cluster of
hit slats along with a single separate slat, we found that the
backup hodoscope information favored assigning the event to the
single slat as often as to the cluster. Events requiring the coarse
hodoscope information were called "saved" events. Four hit patterns
were recognized and classified: 1) a single slat, 2) two adjacent
slats, 3) two slats separated by one blank slat, and 4) three
slats with one imbedded blank slat or four adjacent slats. Each
event had a tracking code (numbered O-8) assigned to each hodoscope.
Odd code numbers (1, 3, 5, 7) were given hodoscope patterns that
didn't require saving and even numbered codes (2, 4, 6, 8) were
the corresponding codes for saved patterns. The code number 0
TABLE III - 3
PHS CLASSES
CLASS CT TFT
I 30 10
II 40 20
III 50 20
IV 60 30
V 60 40
VI 60 40
MULT TAl TASUM EFFICIENCY (TYP)
- 10 95 .998
- 15 95 .980
- 20 95 .969
- 25 95 .910
15 25 95 .792
15 25 100 .771
The Table shows the various cut conditions selected for optimal
A le separation.
All cuts pass eventswhich have a pulse height signal greater than
the value shown. Class II is our choice for the analysis class.
80 81
HODOS~OPE PATTERNS referred to the case where no slats in a hodoscope fired. In Fig.
111-7, typical hit patterns and their code and bin assignments are
shown.
As the Y-hodoscope had no backup coarse hodoscope, optics infor-
mation was used to project an allowed hit range for the +40 mrad to
-50 mrad slits at the spectrometer's entrance. The events resolved
in this manner are the "saved" events for this hodoscope. If no
Y bin showed a hit, the event was assigned a random 6 angle that fell
within the acceptance.
Different tracking criteria can have different r/e mixtures.
Multiple TT events can masquerade as electrons but have a high pro-
bability of giving bad codes (multiple tracks). To examine this, we
first selected events in the analysis class passing the TFT,TAl and CT cuts.
If the event fell above 95 in TASUM it was called an electron and
below 95,a pion. Table III-4 shows p codes vs. 0 codes with the
upper entry being the fraction of PHS analysis class events with those
codes, and the lower entry the a/e ratio.
One sees that the n/e ratio is large away from unique single tracks
i.e., the (1.1) box. On the basis of Table 1X1-4, six code classes
were established of increasing track quality. These are summarized
in Table III-5,whichshows the code class (l-6) assigned to each (P,6) code.
The efficiency for each code class was fit to a second order polynomial
in the counting rate of the APE2 coincidence (a coincidence between the Y
hodoscope, the X hodoscope and TR2), and of the TR2 counter. This tracking
efficiency correction was calculated for each run and applied to the
s1.a; Bin 12 Bin 11
CODE 3 CODE 4 x I 20
-1 1 xx x xx
llllliiiillliiiiiii~ to Two Adjacent Bin 15 or 16 Bin 5 or 6 Slats (Randomly Selected) (Randomly Selected)
CODE 5 CODE 6 x
1 I I 1 I I
'7 x 20 1 XXX 40 Two II -1 Slats Separated Bin 8 Bin 15
CODE 7 CODE 8
Three 1 :.x Y. 20 -1
1 1-1 -YG XYXX
Slats and 1 Bin 7 - 8 Bin 3 zl"ts (Randomly Selected)
ALL OTHER PATTERNS WERE CONSIDERED UNRESOLVABLE
AND LABELED "ZOO EVENTS"
FIG. III - 7
83 82
TABLE III - 4
1 P
e Code ~--+
1 2
0.8176 0.0394 0.0125 0.0007 0.1770 0.4893 0.5532 1.6667 0.0403 0.0041 0.0017 0.0002 0.6839 1.9032 2.6154 5.7500
0.0354 0.0032 0.2900 1.1389
0.0032 0.0004 0.7917 2.7000
0.0018 0.0002 1.5000 2.0000
0.0003 0.0 1.1429 3.0000
0.0012 0.0001 1.7308 4.5000
0.0000 0.0 7.0000 1.0000 0.0004 0.0 1.1250 5.0000
0.0001 0.0 4.6667 3.0000
5 0.0083 0.0008 0.7433 3.1111
6 0.0004 0.0001 2.5556 3.0000
7 0.0027 0.0004 0.8226 2.6667
8 0.0050 0.0002 1.5893 3.2000
p 0 C 01 d e 2
1 3
4
5
6
7
8
>8
3 4 5 6 7 8
0.0048 0.0004 0.7706 1.1000 0.0017 0.0002 2.8462 5.0000
0.0012 0.0000 2.4643 8.0000
0.0001 0.0000 5.0000 8.0000
0.0006 0.0 3.5000 6.0000
0.0001 0.0 2.3333 0.0 0.0002 0.0000 3.6000 4.0000
0.0000 0.0 8.0000 0.0
0.0004 0.0080 1.4444 0.4667 0.0001 0.0003 7.6667 3.1429
0.0001 4.0000
0.0000 4.0000
0.0001 3.5000
0.0 4.0000 0.0 9.0000
0.0 3.0000
0.0004 1.2500
0.0000 8.0000
0.0001 2.0000
0.0 1.0000 0.0000 5.0000 0.0001 5.5000
TABLE III - 5
0 Code ---.-+
0 1 2 3 4 5 6 7 8
1 1 1 1 1 1 1 1 1
1 6 5 5 3 4 3 3 4
1 4 2 2 2 2 2 2 2
1 5 3 3 2 2 2 2 2
1 4 2 2 2 2 2 2 2
1 4 2 2 2 2 2 2 2
1 2 2 2 2 2 2 2 2
1 4 2 3 2 2 2 2 2
1 4 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1
84
>8
1
1
1
1
1
1
1
1
1
data. The analysis stream used only events with code classes 4-6.
The average efficiency for electron data runs was 98% and never
lower than 94%.
ACCIDENTALS
Random master trigger coincidences were created by splicing the
TAlD trigger CT signal together with the rest of the information from
the TA2D trigger. These events were uniquely tagged by the trigger
flags (ORT false and ORA true). Each accidental event that passed
the analysis class criteria (PHS classes 4-6 and code classes 4-6)was
used to decrement the missing mass histogram and final TASUM PHSplot
by 1.176 (this factor is the short spill correction). The accidental
rate was highest for the cross section measuredoffdeuterium at
60 degrees, 19.5 GeV incident. For those settings the number of
accidentals that was subtracted from the analysis class sample amounted
to 2% of the total. For the bulk of the data the percentage contri-
bution was much less than 1%.
OVER-ONE CORRECTION'
We could accept at most one event per pulse as the electronics
had only one set of PHA's and flag units. As counting rates on the
main trigger, ORT, were very low (usually less than .Ol per pulse)
this was not the source of much data loss. Missed ORT events were
corrected for by using the ORTK scaler information. Missed accidental
events were corrected by using the TAZD scaler and a count of the
number of TAZD events read by the computer (gotten by counting events
with a TAZD flag set true). These two over-one corrections were
85
combined in a single correction consistent with the decrementation
scheme explained in the last section:
ORTas (ZEK cp ) - 1.176 TA2Das (TA2Dsc ) Cl = SC: = sfc
ORTas - 1.176 TA2Das
where subscripts as = analysis class event count, sc = scaler
event count, sfc = software flag scaler event count, and the 1.176
is the short spill correction (previously mentioned).
EVENT BINNING
At a particular setting (same Eo, E', 8, and target) there are
20 p bins x 15 B-bins into which events can fall. As a TR2 signal is
required of all events, the p-bin range is limited to 2-19, and the
9 bin range is limited to 2-14. The maximum+ acceptanceis set by the
fixed slit at the entrance to the spectrometer. We required that
-60 mrad < Q < 50 mrad as reconstructed from the hodoscope informa-
tion. Typical p, G and 4 distributions are shown in Fig. III-B.
The solid line on the $J distribution is a Monte Carlo prediction
based on the 1.6 optics (see Appendix D). Similar predictions for
p and 8 were not made as real events are not expected to be uniformly
distributed in p and 8. The solid angle for each of the 234 p- 0
bins was calculated using a Monte Carlo program and stored (on disk)
for both 50 and 60 degrees. Bins of constant missing mass cut across
the p-8 plane diagonally. A particular p-8 bin is included in a mass bin
if its center falls inside the boundaries of that bin.
t
P Hodoscope 1000 Distribution
800 z m ;; 600 5 3 s 400
200
0- I I I 4 8 12 16 20 4 8 12
800
0
P BIN 8 BIN
I I I I I I
Reconstructed + Distribution
- Monte Carlo Calculation
-60 -40 -20 0 20 40 60 4 (mrad)
FIG. III-8
Hodoscope Distributions
16
86 87
The data were taken with overlapping momentum settings of the
spectrometer. This "scanning" was done by lowering the momentum
by one third of the total momentum acceptance for each new setting.
There results a high degree of overlap among the settings comprising
a line. The "counts" (number of electrons) and "weights" (the solid
angle, correction factors, incident flux, etc.) for each missing mass
bin were concatenated over the entire line and subsequently stored
on disk.
RUN WEEDING
There were 1760 runs taken in the experiment. One hundred
thirty runs were found to be unacceptable. Ninety three of these
were abnormally terminated due to major equipment malfunctions or
experimenter error. Twenty one runs were excluded by examining
compatability with similar runs. All runs taken at the same setting
were required to give reasonable x2 comparisons of the cross sections
into the full acceptance. Runs so eliminated were found to have
notes made in the experiment's log books that the beam was mis-
steered or badly focused , the target had problems, or the electronics
or the computer had some minor malfunction. The various run correc-
tion factors were scanned on a run-by-run basis and runs with large
deviations examined carefully. The mean and width of each of the
five PHS's were scanned to look for malfunctioning detectors. Large
jumps in these quantities corresponded to changes in Eo, G and sign
of E'. Tracking efficiency scans unearthed a few runs with dead
hodoscope slats not noted in the log book. These types of comparisons
lead us to discard another sixteen runs.
TESTING THE ANALYSIS PROCEDURE
After run weeding we felt confident in concatenating runs
into settings (i.e., same target, Eo, E' and 0). At this level of
reduction, two tests were made. The first was designed to test
tracking and PHS efficiencies, and the second was sensitive to cross
section variation across the acceptance and setting to setting
compatability.
The efficiency test was easily made. As described earlier in
this Chapter, we derive 6 PHS classes and 6 tracking classes. We
can analyze our data using 36 different criteria with PHS efficiencies
running from 99.9% to 80% and tracking efficiencies ranging from
99% to 80%. The pion contamination varies from several percent
(depending on running conditions) to virtually nil (<.5X) over the
36 PHS tracking classes. The total electron detection efficiency
ranges from lOO%to 64%. The analysis class was selected as the
reference point and the 35 other cross section compared to it.
Table III-6 shows a typical comparison for all the hydrogen running
for E' between 1.200 GeV and 1.400 GeV for electrons at 60 degrees
(the concatenation over E' was done to increase the statistics).
For each line, each setting was so examined. We found no statistically
significant deviation. This leads us to believe we know our
inefficiencies to about 20% of their value for both the PHS efficiency
and the tracking efficiency. As seen from Table 111-6 there is no
definite correlation between PHS efficiency and tracking efficiency.
89
88
TABLE III - 8
MINIMDM CODE CLASS vs. PULSE HEIGHT CLASS
2512.2 2486.4 2445.4 2434.4 2273.4 2054.5 1.001+0.020
0.99706 0.997+0.020 0.991+0.020 0.991*.020 0.988+0.021 0.989+0.022
0.99493 0.98830 0.98386 0.92375 0.83523 0.01832 0.01340 0.00963 0.00942 0.00787 0.00575
2479.3 2454.3 2416.3 2 1.011-&0.020 1.006+0.020 l.OOqtO.020
0.97913 0.97705 0.97056 0.01286 0.01036 0.00741
2459.3 2434.3 2398.3 2387.3 2231.3 2016.3 3 1.018+0.021 1.011+0.021 1.00~0.021 1.00~0.021 1.001+0.021 1.001+0.022
0.96892 0.96691 0.96056 0.95624 0.89777 0.81178 0.00874 0.00683 0.00490 0.00476 0.00400 0.00373
2246.3 2030.3 0.997+0.021 0.997fp.022
0.90710 0.82022 0.00512 0.00457
2277.6 2255.6 2222.6 2211.6 2069.6 1866.6 4 1.011+0.021 1.003+0.021 9.995+0.021 0.995+0.021 0.992+0.022 0.9am.023
0.90972 0.90791 0.90220 0.89816 0.84328 0.76260 0.00201 0.00178 0.00154 0.00150 0.00126 0.00110
2040.6 2021.6 19993.6 1982.6 1853.6 1670.6 5 1.041+0.023
0.79210 l-034+0.023 1.02~0.023 1.025+0.023 1.02~0.024 1.016+_0.025
0.79061 0.78564 0.78212 0.73476 0.66467 0.00083 0.00080 0.00053 0.00053 0.00046 0.00040
6 1968.6 1951.6 1928.6 1918.6 1793.6 1614.6
1.032+0.023 0.77104
1.025.&O.O23 1.018&0.023 1.017~0.023 1.012+0.024 l.OO&M.O25 0.76974 0.76579 0.76254 0.71637 0.64789
0.00056 0.00054 0.00037 0.00037 0.00032 0.00028
The four numbers shown in the Table are: 1) number of electrons corrected for accidentals; 2) ratio to analysis class cross section; 3) electron detection efficiency; and 4) the pion subtraction factor. < E' < 1.4 GeV.
The data were taken on hydrogen with EO= 19.5, 0 = 60'. and for 1.2 GeV
90
Typically, we assign a 3.2% systematic error from tracking and
PHS efficiency.
The second test we made on the data was a cross section com-
parison. Every line with few exceptions was measured three times
in each scan (some of the low E. lines at the low E' were taken in
bigger than l/3 acceptance jumps). Except for the beginning and end
of each line we have three cross section measurements of the same
points which we can compare. A reference cross section is gotten by
concatenating the counts and weights for the three partial cross
sections. This is then compared to individual cross sections.
A x2 test is also made by forming the residuals
U.-U R .= -A-.- 1
iJL4ixi2 ' i and j = 1, 2, 3, i # j
i i
A histogram of the residuals for the 50 and 60 degree data is
shown in Fig. 111-g. The distribution is what one expects normally
distributed data to produce. We conclude that there are no serious
aperture biases in the analysis.
1000 L
1324 RESIDUALS MEAN = -0.063 RMS = 0.964 CURVE=l05.6 cR2/2.
100
I I I I I I I I I I I I I I -3.2 -2.4 -1.6 -0.8 0 0.8 1.6 2.4 3.2
RESIDUAL (o- 1 IbV,l,.
FIG. III-9 A histogram of the residuals Rij. The curve is what one expects . normally distributed data to give.
92 91
CHAF’TER IV
CALCULATED AND MEASURED CORRECTIONS
MEASURED CORRFCTIONS
The full target yields include contributions from the target
walls and from processes which produce both positrons and electrons.
To remove these unwanted contributions we measured these yields
besides the full target electron yields. These were the empty target
cross-sections measured for both scattered electrons and positrons
and the full target measured for scattered positrons. The pres-
cription used to correct the full target cross section is given by
(4.1) +
'COR= 'FULL- 'MT- (0 +I FULL- uMT *
The signal from the empty target typically amounted to about
6% of the full target signal for hydrogen and 4% for deuterium.
The fraction of the measured cross section accounted for by charge
symmetric processes depends on Eo, E', and 0 and in general increases
as E' decreases. This correction,made by subtracting the measured
positron yield from the electron yield, was a primary factor in
determining the lowest E' at which data were taken. Most lines were
run until the ratio of positron to electron yield on the full target
reached .35 (o+&IL/oiLL = .35).
The assumption used in Eq. 4.1 is that there are no important
sources of electrons (other than scattered beam particles) which are
not charge symmetric. A test of this assumption was recently made
experimentally (Ref. IV-l) during the second cycle of E-89 by
measuring the electron yield from the target using a positron beam
and comparing that to the charge symmetric situation with electrons
incident in the same experiment. This wrong sign signal was equal
for the two signs of the incident particle charge to within the
accuracy of that experiment (5% at Q2 = 3 GeV2to 10% at Q2 = 15 GeV2).
For both the empty target and positron signals we make the
hypothesis that the structure in missing mass is smooth. We take
smooth analytic representations of these data as our best estimate
of their actual value. We are assuming that neighboring data points
are not independent but contain similar physical information. Using
the bulk of the data rather than the individual data points can
improve estimates of these corrections.
Plots ofthesedata show that the double differential cross
sections are approximately exponential at these large angles. We
find the following simple parametrization
(4.2) u pas= 106(a + b E,+ c Ez) e -d E'sin e(pb/GeV-sr)
works well for the positron cross sections. The resulting fit
parameters are given in Table IV-1 for the various EO's ,0's and targets.
To propagate the error introduced by these subtractions, we estimate
that the functions thus fitted give the correct cross sections to
(4.3) Au/u = MAX (.l, .3 - .l W (GeV))
This gives an error in this correction of 20% in the elastic
peak regions decreasing to a minimum of 10% for W > 2 GeV. This
error approximation does not significantly improve the errors over
what the measured data would yield. The prescription of subtracting
93 94
TABLE IV - 1
POSITIVE SUBTRACTION
+ + oPOS = 'FULL - 'MT = 106(a + bEo + cEi) e -d Pt (&$)
a b c d x2& 60°, H -13.3290 4.25038 -0.0484835 16.4419 85.71112
60°, D -13.2485 3.76622 -0.0684701 15.1213 1531130
5o", H -19.3759 4.52011 -0.0766568 14.4748 41.1137
50'. D - 9.52999 3.43338 -0.0555869 13.6932 31.0/43
EMPTY TARGET SUBTRACTION
Line E.
1 19.5
2 16.0
3 13.3
4 10.4
5 6.5
6 19.5
7 16.0
a 13.5
9 7.0
%lT
e
60'
5o"
= a e W + cW2) 1 pb \
a
'GeV-sr'
b c x2& O.i60334E-1 -.970139 .536463 la.7124
0.201885E-3 2.59807 -.0407573 15.0/17
0.9028313-2 -.292653 .591770 71.8178
0.1587563-l -.499663 .789576 17.4125
0.250682E-2 2.89575 .179453 92.4163
0.1959943-4 2.62323 .0310931 13.719
0.2689963-4 3.21611 -.0468157 13.2/11
0.6017343-2 .237730 .445982 13.0/17
0.339265E-1 .986842 .521663 12.5119
models allows us to treat all the data in the same manner (we
did not measure all the quantities in Eq. 4.1 for about 30% of the
data, as these corrections were small, and we felt confident in our
ability to estimate them from the measured data). These errors
will be taken as part of the systematic error in the final cross
sections. The X2's quoted in Table IV-l were evaluated using the
statistical counting errors.
An interesting side note and source of puzzlement to us wasthat
the empty target (stainless steel) cross sections were appreciably
different in character from the deuterium cross sections. Our
expectation would be that iron could be well approximated by a
"bag" of deuterons. Fermi motion effects would tend to be similar.
But, the ratio of the iron cross sections to the LD2 cross sections
for wrong sign running is E' dependent, increasing with E'. The
growth is as much as a factor of two for the highest incident energy
lines and always at least a factor of two more than what would be
expected. This means that the size of the empty target cross section
was larger than expected from simple nucleon counting. The corrected
empty target cross section, u& - u + EzT , is the right size for
scattered beam particles, but the charge symmetric part is anoma-
lously large and increases relative to the signal as E' is increased.
We doubt that this effect has been generated by a measurement or
analysis error.
For D2 divide result by l.l6(empty target
only).
95 96
CALCULATED CORRECTIONS
It is traditional to correct the data for the effects of
radiation in the target and in the scattering process itself. For
deuterium, the motion of the bound neutron and proton provide
and additional correction. We have applied three calculated
corrections to this electroproduction data. First, the elastic and
quasi-elastic (as appropriate to deuterium) radiative tails were
subtracted. The "tail subtracted" data were then corrected to account
for radiation which shifts the theoretical electron yields to
higher missing mass. The deuterium cross sections are the source
of the neutron data, and corrections for Fermi-motion effects were
calculated and applied before comparisons with the hydrogen data
were made.
ELASTIC TAIL SUBTRACTION
The elastic tail was calculated by the methods given in
G. Miller's thesis (Ref. IV-2). The elastic tails come from incident
electrons radiating energy through photon emission .and elastically
(or quasi-elastically) scattering off the target particle. The
energy degradation can occur before and after the elastic scatter.
Both produce scattered electrons of lower energy than elastically
scattered beam particles. These lower energy electrons enhance the
cross sections measured at missing masses higher than the proton
mass. The materials in the beam before and after the scatter are
referred to as "real radiators" and are summarized in Table 11-2.
In addition to the effect of this real radiator, there are the quantum
electrodynamic processes involving radiation from the electron
being accelerated during the elastic scatter. This source of
radiation is often discussed in terms of the "internal" or
"equivalent" radiator,as such radiation is similar to that caused
by the real material in the beam. An approximate expression for
the equivalent radiator is
(4.4) teq= % (an (Q2/mz) - 1)
For Q2 = 20 GeV2, t = .04. eq
The expressions given by Tsai
(Ref. IV-3) were used to calculate this correction exactly to
lowest order in a andareused in Miller's approach.
Smaller corrections also included are an estimate of multiple
photon emission and target radiation from the recoiling proton
(only in the case of hydrogen). The elastic tail calculation
requires knowledge of the form factors G E and GM for Q2 less than
the effective Q2 of the point being corrected (the effective
Q2= 4 El2 sin2(8/2)/(1 - 2 E'sin2(G/2)/M)). We have assumed
form factor scaling (GE = G /u Z Gi) and a fit to the measured Me
elastic scattering data for G E ( see Chap. V). The exact expressions
used forthe elastic tails (as well as the inelastic radiative
corrections) are given in Ref. IV-4.
Plotted in Fig. IV-1 are the elastic tail fractions, that
is the elastic radiative tails divided by the raw cross section
for representative lines at 50 deg. and 60 deg. for both hydrogen
and deuterium targets.
98 97
W = 2.5 GeV POINT 6.5 13.3 19.5
20 HYDROGEN ’ I
/
W = 2.5 GeV W = 3.5 GeV For 7.0 GeV For 19.5 GeV
I HYDROGEN ’
12
8
4
0
I I I I I I I I
DEUTERIUM 60" (b)
6.8 0.9 1.0 I.1 1.2 1.3 1.4 1.5 1.6 1.7 E’ (GeV)
O rI ‘1 ” ” ” 0.8 0.9 1.0 I.1 1.2 1.3 1.4 1.5 1.6 1.7
E’ (GeV) 1OICIO
FIG.IV-1
The elastic radiative tail fraction for representative lines at 50" and 60'. Thea= arrows at the top of the graph indicate where a missing mass, W, of 2.5 GeV falls for E,= 6.5, 13.3 and 19.5 GeV at 60° and W = 2.5 for E,= 7.0 GeV and W = 3.5 for E,= 19.5 GeV at 50°.
For the deuterium quasi-elastic peak, we used the procedure
given in Ref. IV-5 (also see Appendix C) to compute the quasi-
elastic cross section which was then radiated to produce a "quasi-
elastic” tail. The Reid hard-core wave function (Ref. IV-6) for
the deuteron has been used in all the smearing and quasi-elastic
calculations.
We take the error in the elastic and quasi-elastic tails to be
the same as those estimated in Ref. IV-4 (55%) plus an additional
MAX(5, Q2(GeV2))% to account for the high Q2 uncertainty of the
squared form factors. This gives + M&X(10, 5 + Q2(GeV2)% error
on the tail subtraction. This error usually contributes less than
2.5% to the systematic error.
INELASTIC RADIATIVE CORRECTIONS
The inelastic radiative corrections are applied to the tail-
subtracted data. This correction accounts for the radiation from
scattersoccurringat low missing mass giving events at higher measllrtld
missing mass. We have used a new technique involving an iterative
procedure with an analytic representation of all data taken at one
angle on the same target.
The exact radiation calculation (as done for the elastic
tails) would take too much computer time (as presently coded).
Instead, an equivalent radiator is used to simulate internal
bremsstrahlung. The hard radiation of this internal radiator is
strongly peaked along the incoming and the outgoing directions of
the electron, hence little angular deflection in tile trajectory of
99 - IO0
RADIATIVE CORRECTION FLOW CHART
the electron occurs. Usually an "angle peaking" approximation
is used which includes only radiation along these two directions.
As the electron can be degraded in energy both before and after the
scatter, we must, in principle, integrate over all E o's and higher
E' s that can contribute to scattering at the measured point.
Examination of this double integration shows that most of the
contribution to the integral comes from either radiation before or
radiation after the scatter, but not both. One takes advantage of this
byan "energy peaking" approximation. The two-dimensional integral
in E o and E' is well approximated by three terms: a) scattering
at the measured E. of the beam with contributions coming from all
allowed higher E's; b) scattering at the measured E' with contri-
butions coming from incident energies down to the lowest allowed
EO's (determined by one pion threshold); and c) scatters in
the"near"region with soft photon emission.
The new technique uses the fact that radiating "known" cross
sections involves only integrals. What is done in practice is to
start with a reasonable model of the data (such as an w' fit
(Ref. IV-7)). Using the model, a radiative correction ratio
R =o rad /a model model-radiated is calculated for each data point,
and a radiatively corrected set of cross sections is formed by
multiplying the data and its error point-for-point by this ratio.
The model is then refit to the data. New radiative corrections are
calculated and reapplied to the tail subtracted data. A flow chart
of the procedure is shown in Fig. IV-Z. The major part of the correction
I u exp (Input)
' = o - 'elastic rare ew tails
'final = 'rare * R
'model = Fit to 'final / I
/ 1 1 Rrad = a-radiation/
1 ofinal /
Elastic Scattering Correction
Model From Previous Data Gives First Estimate of Rrad
Model Radiative Corrections
Refit Model
Form Radiative Correction
Ratio from Model
Check for Convergence
101
FIG. IV-Z
102
The radiative correction ratios for representative incident energies at 50' and 60'. The ratios are ulotted for W>1.75 GdV.
comes from energies near the measured energies,and since the cross
sections are quite smooth, convergence occurs after a few iterations.
The model used has no resonance structure past a W = 2.0 GeV.
Any high mass resonance (W >2.0 GeV) will not have the appropriate
radiative correction enhancement. This probably is a valid assump-
tion as no high mass resonances have been observed for W ~5.7 GeV
for the process e+p + e'+X (Ref. IV-8) for Q2's of approximately
1 GeV'. The radiative correction ratios for some of the lines
are shown in Fig. IV-3. The deuterium ratios are within .02 of
the plotted hydrogen ratios. The formulas used for radiating
the fitted cross sections are given in Ref. IV-4.
Some questions arise as to the correctness of the peaking
approximation used in the radiative correction procedure. To check
its validity, the "exact" (as in the elastic case) radiative correc-
tion ratios werecalculated at some W points spanning the range of the
present data, again using an w' model as the source of the
Wl and W2 structure functions. Two independent programs agreed to
better than 5% with the peaking approximations and the equivalent
radiator used for W <4.5 GeV (Ref. IV-g).
We quote the systematic error given in Ref. IV-4 for the
radiative correction ratio: 53% near threshold (W ~1.3 GeV) growing
to +5% at the lowest values of E'. - This error is considered sys-
tematic and will be combined with the other sources of systematic
6 0.80 F
0.80
0.70
2.0
(b)
I I I I I I I I I I 1 I I I I
2.0 3 .o 4.0 W (GeV)
error.
103
FIG. IV-3
104
SMEARING CORRECTIONS
The deuteron is a very loosely bound structure consisting of
a neutron and a proton. A first approximation for the deuteron
cross section would be the sum of the proton and the neutron cross
sections. This approximation is wrong to the extent that the
motion of the nucleons inside the deuteron distort the free nucleon
structure functions. Structure functions so modified are referred
to as "smeared" structure functions.
The smearing effect is most pronounced for quasi-elastic
scattering where the electron scatters elastically off one of the
nucleons inside the deuteron resulting in nuclear breakup. The
narrow electron elastic peak which results from scattering off free
nucleons is broadened or "smeared out" because of the target
particle's motion.
The smearing correction is done within the framework of the
impulse approximation. The electron is assumed to interact with
only one of the nucleons, the other nucleon being "spit" off as
a free "spectator." Taking the Fermi-motion into account relativ-
istically (that is conserving energy and momentum at all times)
puts the interacting nucleon off its mass-shell. So not only is
the target particle not in its rest frame, but it is off its mass
shell. The first effect blurs the angular resolution of the
scattering and both effects shift the invariant mass of the inter-
action. We follow the proceduregivenin Appendix C to calculate
smeared structure functions from unsmeared ones. The smearing
correction for the inelastic structure functions is often para-
meterized as a smearing ratio, Si = Wli/Wli(SMEARED). More
analysis of the smearing problem is detailed in Appendix C.
The hydrogen cross section subtraction from the deuterium data
was done with a smooth analytic function representing the proton
data appropriately smeared. This procedure is preferable over
point-for-point data subtraction corrected by a smearing ratio.
Smearing ratios are not model insensitive because of the large
kinematic range of the smearing integrals (typically + .2 units
in w' ). The calculated smeared cross sections are less model
sensitive because of this. Forming a smearing ratio reintroduces
the model in a local manner. Furthermore, the same arguments given
for the empty target subtraction and the positron subtraction by a
model subtraction are valid here too. The error assigned to this
procedure was +5% of the up(model-smeared) and was considered
as part of the systematic error in uN* The smeared neutron
'1N structure function can be obtained by subtracting the calculated
smeared proton contribution from the deuteron:
(4.5) wlNc3fhm~) = wlD - wlp(smm~~)
The smearing procedure like radiative corrections is not invertible.
An iterative procedure, similar to that used to account for radia-
tion processes, was used to extract the unsmeared neutron structure
functions. To extract an unsmeared neutron, we have to use the
smearing ratios despite their model sensitivity. The first estimate
105 106
of the neutron smearing ratios are the calculated proton smearing
ratios. This yields an "unsmeared" neutron which generates new
smearing ratios through a fitted model to that neutron data and
so on. A diagram of the logic flow is shown in Fig. IV-4. We
take the error in the smearing ratios to be similar to that cal- f&?
culated in Ref. IV-9 and is typically less than t 1.5%.
The principal problem that arises with smearing compared
with radiation is that smearing extends over a larger kinematic
range (see Appendix C). The principal smearing contribution comes
‘f from approximately +'Z-unit-s-in w' about the w' for which the
calculation is being made. This aspect of smearing makes conver-
gence occur slowly in this iteration procedure, especially for non-
linear parameterizations of structure such as in the resonance
region.
The maximum deviation of the smearing ratios from unity occurs as
x' +1 (Sp= .62 for x' = .92, but for 90% of the data where x' c.8
the ratio lies in the range 0.90< Sp< 1.02). The smearing ratios
calculated for this experiment are shown in Fig. IV-5.
THE EXTRACTION OF Wl
As stated in Chapter I, the large angle cross sections are
insensitive to the value of R: us/ut used in extracting Wl from the
cross sections due to the smallness of E in the measured region.
The contribution of us is always less than 4.5% for R = .18. We
UNSMFARING FLOW CHART
'p Model Fit
ITo uP Data .
Fit Proton Data
i:"::?=!ps1'ps12 F '; Model1
smeared smeared 'D - 'p model
Smear Proton Model
Extract Smeared Neutron by Subtraction
4 U
SN = p model smeared
'p model
Form First Estimate of Neutron Smearing Ratio
Form Unsmeared Neutron
1 I smear
uN model = J d3ps/~p,~z?~ 'N model I
\L SN = 'N model
smear 'N model
Yes
uN Finished
Fit Neutron Data
1 Smear Neutron Model
Form Neutron Smearing Ratio
Convergence
107 FIG. IV-4
108
I .o 0.8
I .6
I .4
0.2
I I I I I
0 0.2 0.4 0.6 0.8
FIG. IV - 5
The smearing ratios (~model/~model smeared)
for the neutron, SW, and the proton, SP.
calculated Id 1 by
(4.6) W1= k? 1 1-e
'mott 2 m&3/2)' 1 + cR
We assign an error of + .5 ER to this procedure, and this error
is taken as part of the total systematic error. A value of .18
was used for R.
SUf?MARY OF SYSTEMATIC ERRORS
Systematic errors of two types are considered: 1) point-to-
point errors and 2) overall normalizations errors. Counter
efficiencies, tracking efficiencies, the pion subtraction factor,
and the fast electronic flag efficiencies are considered here as
sources of point-to-point fluctuations. As it is unclear what
correlations may exist between these contributions, the conservative
approach of adding them linearly together has been adopted. The
detailed contributions and the typicalsizesof the estimated errors
are given in Table IV-Z.
The overall systematic errors which contribute are given in
Table IV-3. In each category the detailed contributions with
typical values of the error are shown. We choose to combine these
errors by adding all contributions to a particular category together
linearly and then combining the various categories in quadrature
(see 83 at the bottom of Table IV-3 ). For the N/P determination
many systematic errors tend to cancel,such as those associated with
the beam, the spectrometer, the inelastic radiative corrections, and
the Wl extraction. Others will partially cancel,such as point-to-
110 109
TABLE IV - 2
POINT-TO-POINT SYSTEMATIC ERRORS TABLE IV - 3
Contribution Size (X)
P D
PHS Cuts: CT .05 .05
TFT .5 .5
TAl .05 .05
TASUM .2 .2
Codes: + Cut .2 .2
p2-19 C"t .3 .3
e '"' 2-14 .3 .3
Code Class 4-6 .5 .a
Flags: ORX .5 .8 STR2 .05 .05
Over One:
Pion Subtraction Factor:
Linear Sum: 3.2 4.3
0.0 0.0
.5 1.0
Category Contribution Typical Size (%)
Beam EO
P D
.8 .8
.6 -6
.2 *2
Target
Spectrometer Solid Angle 1. 1.
Measured Subtraction
Empty Target
Positron Yields
.7
2.
.4
2.
Radiative Corrections
Tails
Inelastic
W1 Extraction
Neutron Extraction
1. .8
4. 4.
1. 1.
P Subtraction
Unsmearing
OVERALL SYSTEMATIC ERRORS
Flux
Halo
Density .5 .5
Purity .5 .5
Length .5 .5
1) Linear Addition
2) Quadrature Addition
3) Contributions Linear, Categories quadratically
4) 3) Added in quadrature to Point-to Point Error
4) For N/P = 6.0%
11.9 12.3
5.0 5.0
6.3 6.0
7.1 7.4
N
3
2
17.3
6.2
7.8
8.9
111 112
point systematics, radiative tails, and the measured subtractions.
For these the average of the P and D errors were used and added in
quadrature with the other contributing sources of error. The
resulting systematic error in the N/P ratio is approximately + 6.0% -
including the point-to-point contribution (+ 4.9% excluding point- -
to-point errors).
These Tables include various kinematic quantities, the
cross sections for P, D, and N, and WI for P and D. Given in
the parenthesis for each P and D measurement are: 1) the statistical
counting errors and 2) the total systematic error for that point.
For the neutron cross sections the "counting" error includes the
5% hydrogen subtraction error added in quadrature to the statistical
counting error of the deuterium cross section.
THIS PAGE LEFI BLAiW
113
TABLE IV - 4
19.5 GeV 50'
3. LOO
3. zllo
3.300
3.400
3.500
3.600
a. TOO
3.800
3.900
4.000
k.&UO
4.200
4.300
4.400
4.500
4.600
3.100
3.200
A.300
3.400
3.500
3.600
3.100
3.800
3.900
4.000
4. AU0
4.ZUO
4.300
*.,uo
4.100
4.600
Q2 (C.3)
24.159 O.L428 0.731) 0.719
24.000 0.1397 0.719 0.701
23.421 0.13b5 0.101 0.683
22.326 0.1332 G.bUl O.bb4
L2.229 0.1299 0.661. 0.645
21.603 0.1213 0.641 O*bLS
20.959 0.1227 ‘,.6&l 0.005
20.298 0.1189 0.600 0.584
19.620 0.1151 0.578 0.503
19.924 0.1112 U.55L 0.542
IB.210 0.107L O.!J.U 0.520
11.418 0.1029 O.lAO 0.496
16.129 0.0986 Il.487 0.415
15.963 0.0943 0.463 0.452
15.178 0.0897 0.419 0.428
14.316 0.0051 0.415 0.405
L x’ x’
PRGTGN
L.Y73 f (0.668. 0.1351
3.2111 t (0.435. 0.1731
3.752 f (0.351, 0.2208
4.616 t (0.330, 0.2791
5.931 * (0.340, 0.3531
7.db9 j (0.390, 0.4431
7.632 f (0.424, 0.5571
10.059 * IOiYOE. 0.7071
12.063 t IO.5811 0.899)
13.680 t 10.673, 1.1551
Lb.486 t lO.U49, 1.5111
19.058 t l1.157r 2.0011
2j.YIb t ll.510, 2.7591
LY.117 * Il.8951 3.9781
L9.083 * l2.b22. 5.990)
39.494 f lb.lEb, 9.4991
d2. (A) dML' Gdf-or -i
DWTFiP.ON
3.90 f I G.dG. 0.22)
3.81 t i 0.50. 0.281
5.10 * I 0.43, 0.351
6.94 f I U.41. U.451
7.93 * I 0.41, 0.571
10.34 * I 0.49, 0.721
13.02 * t 0.59. U.YZJ
16.72 * I G.?4r 1.19)
16.20 f I 0.851 1.561
24.09 t I l.U7r L.UUJ
28.50 f I 1.37, Z.bdl
30.99 * I 1.871 3.461
38.90 * I 2.74. 4.801
51.97 f I 3.69. 0.941
51.20 f I 4.93. IO.491
NwlnoN
1.29 I. I 0.80,
0.69 f I 0.52,
k.i!7 * I 0.47,
2.27 f I 0.40.
2.30 * I 0.50.
3.58 f I 0.59.
4.94 t I 0.72,
7.12 f I 0.89.
b-19 f I 1.03.
lO.bY t I 1.27,
IL.76 t 1 1.59.
IL.46 t I 2.10.
17.36 Z I 2.96.
27.19 t I 3.92.
22.10 t I 5.161
+5.02 * 111.95. 77.90 f I LA. I91 lb.571
0.201 0.04001 * l0.00018. 0.002241
0.26) 0.03933 r 10.00514. 0.0021)bl
0.34) 0.05283 t lO.00443, 0.003631
0.44 I 0.37Ll3 f l3.03430, 0.004651
0.561 J.U82dd t l0.00431. 0.0059lI
0.721 O.IOE5.6 f l0.00510, 0.001541
0.931 0.13732 t lO.OObZO. 0.009671
1.211 0.177Zd t l3.00I81. 0.012631
1.601 0.19388 f l3.00905. 0.016641
2.141 0.15834 f 13.01141, 0.022291
L.721 O.dObU9 t IO.014731 0.02837)
3.591 0.33544 f 10.02025. 0.03743)
4.90 0.42340 t 10.02986. 0.052231
7.211 0.56895 f 10.0403Y. 3.075901
10.911 U.Sb37L f lO.05427, 3.115491
17.25) U.86172 f 13.1~061. 0.13354J
0.03054 f l0.00186. 0.00135)
0.03319 : 10.00449* 0.001781
0.03807 f lO.00364, O.OO.?Zll
0.048U3 f (0.00344, 0.002911
0.06199 r 10.00356. 0.00369)
0.07737 * l0.00410, 0.004611
0.09073 f 10.00447. 0.0058al
0.10064 t 10.00539, 0.007501
0.128J3 t lO.00619. 0.00998)
0.14652 f lO.00721. 0.012378
0.16674 t 10.00914. O.Olb27)
0.20630 f 10.01253. 0.02166)
0.26033 f t0.01644. 0.030031
0.3189b f I0.0207J. 0.043551
0.32021 r (0.02987. O.Obf90
0.43740 f lO.06851. 0.105201
114
TABLE IV - 4
16.0 GeV 50'
2.700 20.291
2.100 19.812
2.9OO 19.323
5.000 lU.616
3.100 18.292
3.200 17.751
3.300 17.192
3.430 16.617
3.500 14.024
3.600 15.414
3. IOU 14.787
3.uoo 14.143
3.900 13.492
4.oou 12.503
4.100 12.107
9* cod, c
0.1732
0.1695
0.1655
0.1614
0.1572
0.1527
0.1452
0.1435
0.1386
0.1335
0.1253
0.1229
0.1174
0.1117
0.1058
x- x’
0.160 0.736
0.740 0.716
0.720 0.697
0.699 0.676
0.677 0.656
0.655 0.634
0.632 0.612
O.bOY 0.590
0.585 0.567
0.5bA 0.543
9.536 0.519
0.511 O.kYS
0.4m5 O.kIO
0.459 0.445
0.432 O.41Y
62”J& dadI’ (o.v-.r)
PIomN
d.LO7 f (1.043. 0.159)
2.UlY * IO.!w8r 0.205J
4.4&k t 10.539. 0.2721
3.967 t (0.344, 0.352)
8.144 t 10.616r 0.454)
10.711 t 10.791, 0.581J
LO.631 f l0.654. 0.742)
15.507 * Il.1441 0.9511
19.349 * 11.4021 1.218J
19.451 f l1.431, 1.5621
Lb.463 t (1.727, 2.025)
30.Y7O t 12.054, 2.672)
3b.ltb t (2.559. 3.6401
39.231 t (3.060, 5.1991
46.201 t 13.885. ?.652J
4.200 11.394 0.0998 0.405 0.3% 5U.7IU f 15.697.12.5621
2rlUU
2. eoo
2.900
3.000
3.100
3.200
3.300
3.400
3.500
3.600
3.700
3.800
3.950
4.000
4.100
4.200
DSPRION tlwmcw
6.22 f i I.L)b. U.ZSt 1.71 t I 1.56. 0.23)
7.40 f I 1.02, 0.33) 5.13 f I 1.04, 0.301
7.63 f 1 0.771 0.4Lt L.41 f I 0.81, 0.40)
9.40 t 1 U-76. 0.551 ‘2.Y5 t I 0.82. 5.53)
11.26 A J 0.83. 0.71) 3.31 t f 0.92. 0.70)
15.21 f I 1.13. O.Y2J 5.48 f 1 1.23. 0.921
19.49 * I 1.>9, 1.201 b.bl t I 1.51. 1.21)
22.00 f I I.61, 1.5dJ 1.74 f t 1.76, 1.61)
24.50 * I 1.87. 2.071 7.47 f t 2.07, 2.121
35.17 f ( i.48, 2.701 h.S2 t t 2.69, 2.761
40.21 f I 3.38. 3.541 15.54 f I 3.61. 3.65)
59.61 f I 4.d4. 4.621 w.75 L I 5.07. 4.79)
57.60 f ( 4.94, b.LbJ 23.03 t I 5.24. 6.52)
57.77 f I 4.dY. (I.971 16.69 f I 5.33, 9.331
81.41 f ( 5.56, 16.561 4U.06 i 1 6.09, 14.111
107.46 f I 1.&G. Lt.771 52.4O t I 8.33, 22.bbJ
0.02IZ8 f (0.00692. 0.00105J
0.01600 f l0.00392, 0.001391
O.il3OJl f I0.00361, 0.00182J
0.34024 t 15.05367, 0.00235)
0.05514 t IO.004191 O.OOJOBJ
0.07309 f 10.00544, 0.0039bJ
0.07303 f l0.00607. O.O05lOJ
U.10715 f (0.00791. O.OObStJ
0.13471 f (0.00975, o.ooa*ti 0.13620 f 15.01002~ 0.01094t
0.1(1659 f 10.01219, 0.01427J
0.21920 f (0.01459, 0.01597J
0.26304 f l0.01931, 0.02604J
0.211270 f IO.02205. O.O3?47t
0.33591 f lO.02521, 0.05702t
0.37116 f 10.04169, 0.091931
0.04130 f 10.01035. O.OOlbbt
0.04935 t lO.00679. 0.002101
U.05Llb f 10.00518r 0.00284t
0.0633s t 10.00513, 0.003701
0.01639 C l0.005bS. 0.004601
0.10381 f l0.00769. 0.0062JJt
0.12667 f lO.03951, 0.0052bJ
0.15259 f J0.011111 0.01091t
0.17249 t l0.01304r 0.01440t
0.24624 f (0.01734. 0.01866t
0.29db2 f 10.02395, O.OZiWl
0.42325 f (0.03436. 0.03292t
0.4119b f (3.03522, 9.04409t
0.4lbtb A 13.03522. 0.06442)
0.63457 f WO4037, 0.09846t
0.7db39 t 10.05706. 0.159301
115
TABLE IV - 4
13.5 GeV 50'
2.400 17.122 0.2030 0.771) 0.746
2.100 lb.712 0.1985 0.157 0.748
L.b(rO lb.205 0.1938 0.735 0.707
2.700 15.941 0.1989 0.712 o.b82
2.500. 15.381 0.1838 0.689 0.662
2.900 14.904 0.1794 U.664 0.639
3.330 14.410 0.1729 0.640 0.616
3.100 13.899 0.1671 0.614 0.591
3.200 13.372 0.1611 u.5nu o.shb
3.wLl 12.828 0.1549 0.562 0.541
3.400 12.261 0.1455 0.535 0.515
3.500 ll.bb9 0.1419 0.507 0.411
3.bOO 11.095 0.1349 0.479 0.4bl
3.700 10.454 0.1278 0.450 G.434
3.900 9.856 0.1204 0.421 0.4Gb
2.400
2.300
2.600
Z.?UU
2.UJO
2.900
3.000
3.100
3.200
3.300
3.430
3.500
3.600
3.700
3.noo
g&i' 2 (&&)
DIOTIRON
5.80 t I 1.91. O.dSJ
7.14 t I 1.5b, U.dOJ
10.40 f 1 1.42, 0.591
11.27 f I 1.26, O.dlJ
lb.17 Z I l.d9, 1.02)
21.26 t I 1.65, A.&Ok
27.61 t I 2.13, A.611
29.90 t I 2.95, 2.20)
39.31 * I 4.11. 3.101
50.47 f I 4.96. 3.771
62.25 t 1 5.95, 4.YbJ
72.39 f 1 5.99, b.tlt
93.15 C I 6.35, 9.lYJ
iOi.11 f 1 0.64. 13.11J
121.10 f I 8.69, 20.24)
PROTOJJ
3.869 t IO.969. 0.2%OJ
4.~95 t tl.109, 0.311J
7.010 t ll.lOkr 0.4061
10.02U t 11.119, 0.501J
11.449 t 11.127, 0.6641
14.362 t (1.241, 0.974)
18.431 f 11.462, 1.09Qt
20.580 t I1.914, 1.368)
24.944 t l2.181, 1.751)
3~.571 * 12.518. 2.284)
41.059 t (3.162, 3.000)
47.265 f 13.504, 3.914)
5d.WY * 13.570. 5.329t
b1.394 t (4.565, 7.605J
73.099 f 16.374.11.205J
NIDmoit
1.51 t 1 1.97, 0.751
L.70 t 1 1.59, 0.141
d.36 t 1 1.41. 0.561
2.53 t I 1.33. 0.79t
5.a t I 1.50, 1.01t
7.50 f I 1.79, 1.281
1U.b) t 1 2.30, 1.65)
3.9s f I 3.1). 2.25)
13.72 f I 4.32, 3.191
IV.49 * 1 5.22, 3.89)
24.93 t I 6.29, 5.14)
LL.04 t I 6.44, 6.96)
3Y.UU f I b.bbr 9.551
31.44 f I 7.41, 13.71t
0.01753 f 13.00439. 0.001091
0.32004 f 0.035051 0.00142t
0.03555 t 10.00543, O.OOlObJ
O,U4615 f 10.00517r 0.002321
0.05330 t (0.00525, O.OOJOPt
0.06736 t lO.DO582. 0.0041OJ
0.00711 t lO.OObOL, 3.00515t
0.091108 f 10.00964. 0.00652J
0.11911 t 10.01049, 0.00044t
0.16262 t 10.01220, O.GLiG7t
0.20063 t J0.01545, O.Olkbbt
0.23304 f J0.01727. 0.01930t
0.26816 f 10.017tb. 0.02652J
0.33854 t 10.02293, 0.0302Ot
0.37079 f 10.03233. O.OSbIkt
0.02b21 f 10.00992, O.OOJIbJ
0.03256 t 10.00712, 0.003668
O.OkttS : lO.OObSk~ O.OOLb9t
0.052OU A 10.005811 0.003721
0.0752b f 10.00649, 0.004741
0.09970 t 10.00775r O.OObOOt
0.13Ob1 t l0.01009, 0.00772t
0.14243 t 10.01404, 0.01049t
0.19881 f ~0.01975, 0.01491J
0.24447 f ID.02404, 0.01527J
0.30423 f (0.02923, 0.02424t
0.35940 t f5.02955, 0.03307t
0.46352 t 10.03012, 0.04571J
0.50791 f (0.03334, O.Gbb17t
46.00 * I 9.54. 21.07) 0.61429 Z 10.04406. 0.10269t
116
TABLE IV - 4
7.0 GeV 50'
2.000
2.103
2.ZOJ
2.300
2.400
2.soo
2.bOJ
2.700
2.8UO
2.900
2.000
2.100
2.200
2.350
2.4OJ
2.500
2.600
2.700
2.000
2.930
7.283 0.3058 0.700 0.645
6.985 0.2950 O.bb4 0.613
6.672 0.2835 O.bLU 0.580
6.345 0.2713 o.svo 0.545
0.003 5.2583 0.552 0.510
5.647 0.2446 0.513 0.475
5.27L 0.2300 0.473 0.438
4.B91 0.2lYb 0.433 0.4oL
4.491 0.1984 0.392 0.304
4.076 0.1913 0.351 0.326
PROTON
bV.54 t I 6.57, 4.321
le.05 t I 7.14. 5.74)
llL.9b f 1 9.551 7.551
155.33 f 111.11. 10.101
Id,.54 t 112.03. 13.33)
23l.Ub t 113.94, 17.2bb
3UO.bl t ll4.80, 22.73)
381.d> A Ilb.35, 30.751
COO.71 t 119.41, 40.381
53a.56 t 128.07. 56.811
0.37247 f 10.33685. 0.0045OJ
0.08693 f 13.00158. 0.00609J
O.l;L191 f l0.0103L. 0.00815J
0.17095 t 10.01223. 0.01111t
0.20830 f IO.01350. 0.0149bJ
0.272b3 t IO.01598. 0.01979)
0.35208 f lO.01734. 0.02662J
0.464555 f 10.01959, 0.03683J
0.56482 f 10.02380. 0.0495Ot
0.67385 * (0.03526. 0.07134J
DWTERON NIOTION
97.33 t I 7.17. b.341 3L.GL t I 8.82. b.kbJ
139.14 * 4 8.49. 8.391 4Y.09 t I 9.bl. 8.631
189.78 t Ill.301 ii.5bb 74.40 f 112.77. 11.97)
224.46 f lll.L3, lb.031 75.94 t 114.42, 16.671
271.43 t (16.83, 21.blJ hf.17 t 116.87, 22.52)
368.26 t 117.44. &Y.bCJ 133.57 t 121.24. 30.801
472.b8 t 121.J5, 3d.001 lU>.2> t 125.85, 39.611
558.90 f 124.17. 40.41) 204.17 t (30.39. 5O.JlJ
700.62 : 125.09, 63.14J 270.59 t 133.62. 66.131
U.10144 t 10.00810~ 0.00661J
0.14154 f 10.00900r 0.0089ot
0.20493 f 10.01220. 0.01248J
0.24703 f l3.0134b. ').01765t
U.30472 k 10.01553r 0.02426)
0.422lJ f 10.01999r 0.033961
0.55362 * lO.02465, 0.044511
0.66945 t JO.02895. 0.05799J
0.15UY5 t lO.03376. 0.07814J
763.00 * 135.12, 83.951 dku.80 t 145.74, 86.84t 0.95934 t l0.04486, 0.105431
117
TABLE IV - 4
19.5 GeV 60'
(0%
2.000 3u.544 0.1151 0.907 0.884
2.100 30.170 0.1137 0.395 0.012
2.200 29.779 0.1123 O.Utl3 0.860
2.300 29.367 O.llOLI o.(lt49 0.847
2.400 28.93Y 0.1093 0.656 0.834
2.500 2U.491 0.1077 0.841 O.tJLO
2.690 2Y.026 0.1060 O.UL7 0.806
2.100 27.543 0.1043 0.u11 0.791
2.800 27.041 0.1025 0.795 0.771
2.900 26.521 0.1006 0.779 0.759
3.000 25.913 0.0986 0.762 0.743
3.lhlO 25.426 0.0966 0.744 O.tdb
3.2&J 24.1152 0.0945 0.72b 0.708
3.300 24.259 0.0923 0.709 0.690
3.400 23.648 0.0901 O.bU9 0.672
3.500 23.U18 0.0870 O.bbV 0.653
3.603 22.370 0.0554 0.649 0.633
3.700 21.704 0.0929 0.629 0.614
3.800 21.020 0.0504 0.606 O.SY3
3.900 23.311 0.0178 0.5011 G.572
(0% L.OOU
2.100
2.200
2.300
2.400
2.500
2.600
2.100
2.600
2.voo
I*000
3.100
3.LGO
3.300
1.400
3.500
3.600
3.700
3.nohl
3,900
DJNTIRDN nNoTaoN
0.145 t 10.019, 0.0101 U.009 I (0.016, 0.0041
0.176 i 10.019. O.OlYJ O.OlA t 10.016. O.OObJ
0.305 f 10.0231 O.Olf) 0.051 f IO.0201 0.009,
0.334 2 l0.025. O.OLPJ 0.053 t 10.027, 0.013J
0.429 f tO.OZII, 0.0261 O.UZa f IO.032, O.OUt
0.484 f 10.533, (1.0371 U.063 t 10.0381 0.02bJ
0.682 t l3.041e O.GkUJ 0.130 t 10.048, 0.031)
0.026 t lU.049, O.Ub21 0.155 t l0.055, 0.0491
1.344 i 10.065r 0.0811 0.454 f 10.075. 0.0671
1.342 2 (0.014. G.lObJ 0.302 t to.018. 0.0911
1.774 i (0.095~ 0.1381 0.417 t l0.113~ 0.123J
2.306 i 10.127. 0.102) 0.703 t l0.148, 0.166)
2.559 i t0.156, lhZ3VJ 0.647 t t0.133. 0.2241
3.620 t IU.lPBt O.dl7J 1.22b f 10.229, 0.302)
4.505 t JO.Zdllr 0.4211 1.597 t 10.277. 0.4031
5.672 L IO.Pd2. O.LboJ 2.154 t (0.3311 0.5571
7.032 ; 10.3311. O.tblJ 2.791 t (0.399. 0.7571
8.611 i 10.416, l.Ojlt 3.137 t 10.48S* 1.037)
9.785 * (0.573, 1.417) 1.121 f 10.650, 1.4311
11.749 t dO.Ltl, l.YIIdJ 4.312 t lO.bIOv 2.025)
&a dMP'(O.V-.r)
PROTON
0.053 i JO.010, 0.0041
cJ.OLj t 10.011. 0.0061
0.131 f 10.015. O.OOSJ
0.140 i IO.016. O.OlOt
0.144 t lO.020, 0.014t
0.304 t 10.024, 0.0191
0.379 i 10.0301 0.025)
0.563 t 10.037, 0.034)
0.116 f 10.044, O.MIJ
0.922 f 10.059, 0.0601
1.039 t l0.067, 0.0791
1.183 t lO.0901 0.105J
l.U25 t 10.119. 0.1381
L.311 i lO.L471 0.191J
2.997 t 10.150, 0.238t
A.506 i 10.L01, 0.315t
4.730 t 10.234. 0.418)
5.679 t (0.266, O.SbOt
6.343 t 10.346, 0.7601
7.509 t (0.346. 1.051J
$&I (o&r)
0.00079 f 10.000151 O.OOOObI
0.00080 t 10.00017. 0.00001J
0.00196 t 10.00022. 0.OOOllt
0.00210 f 10.00024. O.OOOlSt
0.00367 f 10.00031, 0.00021J
0.004511 t l0.00037r 0.00025t
0.30573 t l0.00045, 0.000311
0.00852 i 10.00056, 0.00051J
O.OlOt3b f ~0.00067, O.OOOb1J
0.01402 i 10.0001)4, 0.00091t
0.01585 i 10.03102. 0.00121t
0.02114 i 10.0013lr O.OOlbOt
0.02791 i l0.00153r 0.00211t
0.03562 i l0.00226, 0.00279t
0.04620 t l0.00271. 0.003bSt
0.05423 i l?.OJ311* 0.004871
0.07339 i 10.00362, 0.0044W
O.iNNN i 10.004141 0.00870t 0.09906 i (0.00541. 0.0118bt
0.11758 f 10.00542. O.Olbkbt
0.00211 i 10.00028. 0.000151
O.OOZbk t IO.000211 0.00019t
0.00456 t 10.00034, 0.00025t
0.00505 t 10.00037, 0.00032t
0.00645 i 10.00042~ 0.000421
0.00729 t t0.00049, 0.00055J
O.OlOZY i 10.00063, 0.000721
O.OlZbL i ~0.00074r O.OOf-+t
0.02039 f JO.00091r 0.001.4t
0.02041 t 10.00112, O.OOlblJ
0.02705 t lO.00145~ 0.002llt
0.03526 a lO.OOL14, 0.00278t
0.039bV t 10.00240, 0.003611
0.05545 t 10.00304, O.OOlltJ
0.06945 A (0.00367r 0.00449t
0.09169 t (0.0043br 0.001TIt
0.10906 t IO.00524, O.Oil@Ot
0.12396 t lO.OObk?t O.OlbO4t
0.15272 i 10.00194, 0.02212J
(r.lYO94 2 (0.00591, 0.03lObt
118
TABLE IV - 4
16.0 GeV 60°
&, Q2 oa.?)
2.000 24.305 0.1336 O.&l85 O.YSiJ 0.202 t ~O.OZlr 0.0121
2.100 23.715 0.1317 0.870 0.843 u.34z * ~O.OZ7, 0.010
2.200 23.533 0.1197 0.555 o.uze 0.441 f (0.033, 0.0231
2.330 2z.vao 0.1276 o.u39 U.813 0.5b5 * (0.043, 0.0321
LA50 21.509 0.1254 0.822 0. 1Pb 0.74M L l0.05b. 0.045i
2.500 22.071 O.lZ3l 0.004 0.779 1.135 t 10.075, 0.0611
2.600 21.614 0.1207 0.786 0.762 1.327 t (0.090, 0.084)
2.lDO 21.140 0.1152 0.7b7 0.744 1.672 t 10.120, 0.1134
2.900 20.b4.5 0.1155 0.74Y 0.125 2.439 t (0.156, 0.1521
2.900 20.137 0.1128 0. IL5 U.7li5 hOY7 t (O.IPb, 0.2041
~.OOO IP‘LO9 0.1100 0.707 V.6UU L15J f lO.ZZlr 0.271)
3.100 19.013 0.1071 0.6Ob 0.4b3 4.613 r JO.ZbZ., 0.3591
3.200 18.499 0.1041 0.664 O.b44 5.516 t 10.323. 0.4771
ha00 17.911 0.1009 0.642 O.bZZ 7.5lr t (0.450, O.b94I
3.406 11.~19 0.0977 0.619 O.bOO 9.525 t tO.ttb. 0.0521
2.500 lb.700 0.0944 0,595 0.571 L&.lUP t 10.77bl 1.159I
2.UJU 0.425 t dU.UJZ, O.ULSJ
2.100 0.574 f JU.Ub7, 0.0311
2.200 0.730 f 10.046, 0.045J
2.500 0.942 f tO.ObO, O.ObO)
2.400 1.243 t 10.080. U.OYOJ
2.500 1.710 2 10.102. O.lObi
1.600 1.916 5 (O.llb, U.A4AJ
2.740 2.734 t lO.l4dr O.liJPJ
2. a00 3.600 f (O.ld5, 0.25rh
2.400 4.799 * i0.&?1, 0.358J
3.000 5.753 f to.2651 0.4531
3.100 7.Zl5 f 10.307. 0.6111
3.200 8.798 f l0.360. 0.11311
3.300 10.559 t dU.4JY. I.1141
3.400 14.049 * iO.UJd, 1.54bJ
4.500 17.185 f 10.052, et.1741
0.055 t lO*O~h, 0.0141
0.094 t (0.042, 0.011)
0.1&b * 10.053, 0.0301
0.174 * (0.069, 0.043)
O.&O i 10.091, 0.062J
0.442 t 10.117. 0.007J
U.JbO t lO.lJtr O.lLlI
U.7AL f JO.llbr O.lbOj
1.087 f l0.220* 0.233)
l.b4l f JO.2701 0.3lIl
1.451 t (0.327. 0.435)
L.3Y3 t IO.3181 0.597J
d.Yl2 t (0.465. Od24l
A.*07 t 10.609. I.LA71
5.LJO f 10.9431 1.564)
b.Z89 f 10.943, 2.218)
0.00199 f l0.00020, u.ooo11j
0.00355 t 10.0002b. 0.00016J
0.00455 : IO.00052, 0.00023)
0.00550 f (0.00043. 0.00032j
0.00741 : l0.00056r 0.00044~
0.0113Z f (0.00074, O.OOOalJ
0.01324 2 l0.00090~ 0.000841
0.019r3 * IO.00123, o.oollm~
0.02449 L lO.OOl5b. 0.00153l
0.05111 t 13.001971 0.00205J
0.03191 r J0.00224r 0.00274J
0.04744 : 10.00266. O.OOlb5J
0.05622 t 10.00529, O.OOWb~
0.07754 t lO.O049I, O.OOb49J
0.09790 t JO.O0797* D.00575J
0.114b5 t tO.00500~ 0.011911
0.00416 t 10.00032, 0.000251
0.005b4 t 10.00036, 0.00038J
0.00720 t t0.00045, 0.00044J
0.00931 t ~0.00059, 0.00059J
0.01232 t 1o.ooot9, 0.00019I
O.OA700 t lO.OOlOZ, 3.OOlObJ
U.Ol9Il t IO.OOLlb, 0.00141I
0.01735 : ~0.001491 0.001091
0.03bZZ t 10.00155, 0.00255J
0.04835 * ~0.00225* o.ooa401
0.058IU t JO.00269. 0.004581
0.07323 & (0.00311. 0.0062OJ
O.OWbb t 10.00367, 0.00047)
0.10804 f l0.005011 0.0114OJ
0.14436 t :0.00554* 0.015.7J
O.L7733 2 l0.008%8, 0.022431
119
TABLE IV - 4
13.3 GeV 60°
2.000 lV.120 0.1523 O.dbO 0.827
2.10* 18.761 0.1497 0.84L 0.810
2.200 18.384 0.1469 0.825 0.79.?
2.300 17.990 l.1440 o.uo3 0.773
2.430 17.578 0.14OY 0.783 0.75)
2.500 17.145 0.1377 0.762 0.733
2.bOo lb.702 0.1343 0.740 0.711
Z.?OO 16.237 0.1308 0.717 0.640
1. I500 15.755 0.1271 O.bo* 0.661)
2.900 IS.256 0.1233 0.670 0.645
3.000 14.739 0.1194 0.645 0.621
3.100 14.204 0.1153 0.619 0.5YO
5.&O 13.652 0.1110 0.593 0.571
5.300 13.053 0.1066 0.567 0.54b
3.400 12.495 0.1020 0.539 0.519
6'0 (-i&j d20 XE' CeV-sr (A) dME' cev-sr
1.000
2.100
2.200
2.500
et.400
2.500
2.000
2.100
Z.dOO
2.400
3.000
3.100
3.LOO
a.aotl
Ot.OTNNON
1.198 t lU.OdP, 0.0851
1.635 f lO.OYZ. 0.127r
2.267 f LO.121. 0.152J
2.802 f lO.l‘tL)r 0.1831
3.501 * lO.IUL, 0.2971
5.020 f lO.L47. O.J5bJ
5.938 f 10.3Z8, 0.5741
8.229 t 10.420. 0.701)
10.704 f (0.561. ti.8511
12.725 f lO.0>7* 1.36‘a1
18.025 f lO.U54r A.7711
22.619 k 11.255, Z.lOjl
28.236 f (L.ld3, 2.8151
33.456 A l4.Zt.5, 4.5221 12.na4 f (4.399, 4.671)
d2a zizJP(C.V-rr I& )
PWION
0.656 L 10.066. 0.043)
(r.YIJ f IO.0691 0.064J
I.341 * (0.093. 0.128J
1.189 t lO.114* 0.164)
L.455 f l0.149, 0.1731
3.049 t 10.183. 0.1371
3.7% f IO.ZZ7. 0.355)
4.d49 J: 10.313, 0.575J
b.611 t (0.469. 0.8OlJ
U.dL3 f (0.646, 0.9blJ
LA.U55 t IO.8771 J.OLTl
lb.bO3 t lL.247, 1.2801
17.300 9. ll.321, 1.846)
24.100 f (1.264, 2.4441
29.057 t lL.518, 3.1611
0.220 t (0.104. 0.013)
0.364 k (0.108, O.LOOJ
0.600 f (0.142. 0.127)
a.690 f 10.177. 0.1611
0.~03 f l0.222, 0.2701
A.510 f (0.298. 0.3341
1.500 f 10.589. 0.5491
2.573 t (0.519. 0.6851
3.576 f IO.bbL. 0.5451
3.605 t 10.793. 1.3691
b.VL4 f il.0191 1.7961
0.909 f. 11.435. 2.151J
ll.405 f lL.348, L.8971
0.00434 f 10.00044r 0.0002aJ
0.00622 t JO.000461 0.00042J
0.00391 t 10.00062, 0.00005J
O.OlLLb f 10.00076. 0.00109J
0.01644 f l0.00100. O.OOllbJ
0.02065 f lO.OOl23r 3.001591
0.02562 f l0.00154, O.OOZLOJ
0.03292 f 10.00212, 0.003931
0.04509 f l0.00320. 0.00546)
0.0604d jz 10.00443, O.OObb3J
0.001t.9 t lO.OOb04. 0.00701J
0.11641 f J0.00.564. 3.00587J
0.12052 f lO.00921. 0.0128bJ
O.lb&W f L0.00886. 0.017L3J
0.20480 r L0.01070, 0.022281
0.00790 t IO.00059r 0.000561
0.0105z f ~0.000611 0.00014~
0.01501 f 10.00081. 0.00101J
0.01069 f J0.00099. 5.00122J
0.02345 t 10.00122. 0.00199J
0.03375 f t0.0016b. 0.0024OJ
0.34012 f ~0.00220, 0.0038Il
0.05586 f l0.00298, 0.0047bJ
0.07301 f (0.00382, 0.005801
0.08723 f 10.03453. 0.00935)
0.12421 t lO.O05BU, 1.012ZOJ
0.15671 f 13.00LJ70. 0.01457J
0.19671 f lO.O1521* 0.019blJ
0.23441 f 10.02988~ 0.031681
120
TABLE IV - 4
10.4 GeV 60°
2.000 13.u90 0.1793 O.d17 0.776
2.100 13.543 0.1742 0.79) 0.734
2.200 13.119 O.lb99 0.769 0.731
2.300 12.197 0.1694 0.144 0.758
2.400 12.399 0.1606 0.711 0.683
2.300 11.984 0.1337 U.6YI 0.631
2.bUO 11.332 0.1303 O.bb5 0.631
2.700 Il.103 0.1430 0.634 0.604
Z.YOO IO.637 0.1393 0.604 0.376
2.YOJ 10.134 0.1334 0.514 0.341
3.000 9.633 0.1272 0.343 O.blcl
3.lUO 9.130 0.1208 5.311 0.497
Z.OOU
2.100
Z.LUO
2.300
2.400
2.500
2.600
2.700
Z.YOO
2.905
3.uou
3.AUO
Ll- NXJJ3XON
4.77 t 1 0.31. O.LdJ I.12 t ( 0.36,
6.81 k I 0.59. 0.591 l.YJ f I 0.45,
9.38 t 4 0.501 0.531 3.13 f 1 0.391
12.2Y f 1 5.63. 5.74i 3.94 2 4 0.75.
IS..34 * 1 0.80. l.OLJ 5.05 f 1 5.94,
19.61 f 1 o.e.1 1.42) 5.66 f 1 1.18,
26.43 t 1 J.1t.t l.YYJ 9.23 t 1 1.46,
33.17 k I 1.49, 2.721 12.30 * 1 1.M.
43.82 2 I 2.02. 3.n4t 14.29 f 1 2.49,
36.95 f 1 2.92, 5.38) L1.3.? f 1 3.44.
60.62 f I 4.54. 7.UJJ 24.47 t 1 *.95,
95.90 t 1 9.25. IO.441 5o.dU f 1 9.70,
PJtMW
5.566 t 10.242. 5.1851
4.329 f 10.303. 5.23OJ
6.335 2 15.457, 5.34dJ
Il.826 f 10.323. 0.3531
11.032 t 10.634. 0.6821
L4.77I t to.798. 5.907)
11.645 * 10.918. 1.2461
23.321 t ll.049. 1.671J
30.576 t 11.213, 2.303)
.r7.034 f 11.718, 3.1431
47.307 f 12.438, 4.403)
53.9ZU t 14.701, 6.120)
0.24 I
0.33)
0.49)
0.701
5.99 J
1.41)
2.011
2.771
3.94)
5.531
O.lLl
10.85)
0.01195 f 10.50094, 5.50072J
5.51773 f ~0.001191 0.00098i
5.52316 f ~0.551blr 5.00136J
u.03301 f LO.032Od. 5.052OOJ
0.04533 t lO.OOZbL, CJ.002721
0.03941 * 15.50321. 5.00361)
0.07346 f 15.50372, 0.00303)
0.09393 t 15.00428. O.OOb1)ZJ
0.12365 r 10.00323, 0.009471
0.13399 t 10.53712r 0.01333~
0.19Ukl f 10.01013, 0.010391
0.22713 j. lO.01985, 0.023181
J.01865 f C0.00121, 0.50109l
O.UZbfO f 15.00132, 0.00134J
0.03776 f l0.00199. O.OOZlOl
0.011177 f 10.00231. 5.002931
0.06321 f 15.00319, 0.00407J
0.07891 f lO.UO391. 0.50372~
0.15700 9. 15.00469. 0.50807J
0.14342 f 10.00608, 0.01111)
0.18009 * 10.00131, 5.01377I
5.23573 t J0.01258, 5.52229l
O.LIbbU f 15.51815. 5.53271J
0.38286 f ~5.53896, 0.043981
121
TABLE IV - 4
6.5 GeV 60'
1.073 9.251 0.2838 0.971 0.669
1.100 9.209 0.2827 0.963 0.804
1.123 9.lbb 0.2816 0.960 0.879
1.120 9.122 0.2805 0.934 0.873
1.171 9.07r 0.2794 0.948 U.BbLL
1.200 9.031 5.2702 0.942 O.BbL
l.&?S a.984 5.2770 0.935 0.851
1.230 0.936 0.273b 5.V29 0.851
L.L73 u.ee7 0.2745 0.923 0.843
1.300 6.037 0.2732 0.916 3.b39
1.325 8.786 5.2719 0.909 0.831
1.330 0.734 0.2706 5.v53 o.t121
1.373 8.681 5.2692 0.896 U.&i1
1.450 8.627 0.2670 0.869 0.815
1.425 8.572 0.2664 0.882 0.8Oll
1.430 u.317 0.2649 o.n73 0.802
1.475 a.460 0.2634 O.(Lbl 0.7cz
1.505 8.402 5.2119 O.SbO 0.7UY
1.225 u.343 5.2604 O.l&! 0.782
1.530 8.204 0.2380 0.945 5.775
1.373 8.223 0.2572 0.837 0.766
l.OJO b.162 0.2336 O.b.?P 0.161
l.OL5 b.599 0.2339 0.8&l 0.754
l.bSO 8.036 5.2322 5.814 5.141
1.673 7.971 0.2303 o.mo!l 0.140
1.700 7.956 0.2487 0.797 0.732
l.723 7.839 0.2469 5.769 0.723
1.755 7.772 0.2431 O.lb1 0.117
1.773 7.103 0.2432 5.77L 0.710
1.800 7.634 0.2414 U.764 u.IU.2
1.ac5 7.364 0.2394 0.755 5.494
1.850 7.492 5.2373 0.147 U.bdb
1.873 7.420 0.2355 0.138 O.L79
l .YOO 7.347 0.2335 0.729 0.671
l.Y.25 1.273 0.2314 U.710 0.662
1.950 7.197 0.2294 5.711 0.054
1.973 7.121 0.2272 O.75L O.b4U
Q2 (0.V2)
c x’. x’
PROTON
-O.LlB t 10.206,-5.0001
0.257 t tO.L33. 0.0761
5.342 f (0.248, 0.082)
0.962 t 10.261, 0.0941
0.442 * JO.LOO~ 0.0741
1.354 i 10.277, O.llOJ
1.679 t 10.282, 0.1241
2.068 r (5.287. 5.131)
2.484 t 10.303, 0.1471
3.469 t 15.340, 0.1861
A.000 z 10.322, 0.170)
4.014 t ~0.332. O.ZllJ
4.442 L (O.db2, 0.231J
!&be3 t 10.422, 0.2831
6.4lY f 10.424, 0.3191
b.9b7 f 10.464, 5.343J
9.519 * (0.5651 0.4311
13.247 t JU.644, 0.6OYJ
ld.t)YS f. (0.679, 5.6431
11.633 * 10.620, 0.5591
AU.733 t 10.611. 0.530)
11.903 f 10.638, 0.388J
AL.925 i 15.669, O.bClJ
17.549 * 10.1)09, 5.8471
LA.931 * IO.9441 1.046J
~3.538 f 11.013, 1.216)
24.795 f li.026, I.2021
Z&A50 t 11.084. 1.375)
db.i!&U t 11.579, I.3081
L7.751 f 11.132, 1.396)
dl.4bl t Il.2311 1.385)
3L.lbY t 11.308, 1.6451
36.085 f (1.431. l.BSLJ
31.611 f 11.337, 1.9371
43.bb2 t (1.734. 2.1661
43.12Y f 11.823, 2.3821
5L.U44 f 11.942, 2.738)
-0.05028 f J5.50027.-O.OOUOOJ
0.00027 t IO.000301 O.OUOlOJ
0.00571 t (0.05032. O.OOOllJ
0.00126 A (5.00034. 0.000121
0.00058 f 10.00026, 5.000101
U.55198 2 10.50036. 5.050141
0.00241 f ~0.05037. 5.055161
5.00273 f ~0.05038t 0.00017~
0.003211 f 15.00040. 0.00019J
0.50462 f 10.500431 0.50025J
0.053Yd f 10.00543. 5.000LPJ
0.50534 * 10.055471 0.0002e~
0.00596 t (O.OOUCB, U.OOO31J
0.50759 t 15.00036, 0.000381
0.05867 f J0.00037, O.OOMIJ
0.05935 t IO.OOObZ, 0.500461
0.01280 f 10.05073r 0.000611
O.OL78d f J0.50087. 5.00582J
0.01877 f 10.00092. 0.000871
0.01575 f 15.00084, 0.5007bJ
0.51457 f 10.05083, 0.00572)
0.01625 t l5.05089, 0.000801
0.017bS f 10.00091. 0.00587l
0.32433 f 13.30111, 0.00116J
O.J35#7 f ~0.00129, 5.50143)
0.03511 + J5.00139, 0.00167J
0.03418 f (0.00141, O.OOlbbJ
0.03Yl9 t 10.05133. 0.05190l
0.03bQQ t IO.00150, 0.051811
0.53858 L J0.0515lr 0.001941
0.94363 t 13.00172. 0.002211
0.54490 t lO.O51t)31 0.05230J
0.05060 t lO.UO203, O.OOZbOJ
0.03290 f J0.50219, 5.002751
5.06145 t lO.ODZCS, 0.0032OJ
5.0638S f 13.33258. 5.00337)
0.57359 t 15.50276~ 5.003891
122
(CL,
2.000
2.150
2.200
2.300
2.4OU
2.3UP
L.bJU
2.U00
2.100
2.250
2.350
2.400
2.305
2.600
Q2 (G.V2)
7.044 0.2231 0.69J 0.63U
6.726 0.2161 O.b3b 0.654
6.392 0.2066 O.blU 0.569
6.043 0.1965 0.37a 0.533
Lb79 0.18511 0.530 U.496
3.29a 0.1744 0.497 0.439
4.903 0.1625 0.*35 0.420
TABLE IV - 4
6.5 GeV 60'
x- x’
DRUZERON NWIRON
77.44 f I 1.74. 4.901 25.7d 9. I 3.47. 4.97)
103.32 f 1 &Ode 1.251 Al.97 * ( 4.141 7.44)
140.00 f t 3.30. 9.11OJ 47.06 f ( 5.94, 10.14)
195.14 f I 6.14. 14.391 68.91 * 1 8.73. 14.96)
244.67 f ( 7.42, 25.411 89.53 L 110.92, 21.29J
311.06 2 I 7.42, 25.401 114.83 t JlZ.Sb. 26.501
391.62 f I 1.42, 3L.331 446.16 i (14.69, 32.68)
& (a 1 dGd2’ Cd’-8r
PWTON
IS.29 t 1 1.07. 3.32)
75.04 f I 1.16, 4.631
97.71 f 1 1.43, 6.381
120.22 t I 2.77, 9.291
157.98 t L 7.13, 13.631
~0L.57 t Ill.401 21.27)
dud.77 t 116.48, 25.331
0.01813 f 10.00132. r).OO473J
O.lOU25 f lO.OOlblr Q.OObb9J
5.l4291 f I0.00213. 0.009631
U.19522: i 10.00412r 0.0137OJ
0.23798 f (0.01077. 0.02033J
U.31501 f (0.0174S. 0.0325fi
O.C492I f l3.02563r 0.039421
O.l lOA5 f J3.55248. 0.50698J
5.14903 f 10.00293~ 0.01046J
0.20392 f ~0.05512. 0.01434J
0.282ia f ~0.00911. 0.52133J
0.36837 t tO.Olll~r 0.030738
0.47bOk f lO.O113b, 0.039881
3.60930 f ~5.01155~ 0.54177)
123
CHAPTER IV - REFERENCES INTRODUCTION
1. L. S. Rochester et al.(to be published).
2. G. Miller, Ph.D. Thesis, Stanford University, SLAC Report No. 129
The measured cross sections at 50° and 60' cover a wide range of
kinematics and give new information about the nucleons for both elastic
and inelastic electron scattering. A general form of the cross section 2 2 2 (1969); also
(1971).
3. L. W. MO and Y. S. Tsai, Rev. Mod. Phys. 41, 205
Y. S. Tsai, "Radiative Corrections to Electron SC
SLAC-PUB-848 (1971).
attering,"
4. S. Stein et al., SLAC=PUB-1528 (1975).
5. W. B. Atwood and G. B. West, Phys. Rev. Dl, 773 (1973).
6. R. V. Reid, Jr., Ann. Phys. (N.Y.) 2, 411 (1968).
7. J. I. Friedman et al., SLAC-PUB-707 (1971).
a. R. L. A. Cottrell et al. (to be published).
E. Allton, private communication.
CHAPTER V - RESULTS AND CONCLUSIONS
(5.1) a = e anaEr I,E 2 sin40/2
0 tan2U/2 )
indicates that for small angles and energy loss the measurements will
be dominated by the behavior of W2. W2 has been carefully measured
in previous experiments (Ref. V-l). For the measurements reported
here at large angles and energy losses the contribution of Wl to the
cross section is much larger than that of W 2’
In a composite model of the proton (with spin l/2 and spin 0
constituents) W 1
is determined by the scattering from the particles
with spin l/2, but for W2 particles of both spin 0 and spin l/2 can
contribute. Thus in a simple quark model Wl directly measures scatter-
ing off the quarks, where W2 might contain contributions from spin 0
"glue" particles.
The measurements at 50' and 60° were carried out in a region where
the total mass of the recoiling hadronic state is small compared with
the momentum transferred to it. (This region is referred to as the
"threshold region"). Because of kinematics, the fragments all travel
away from the collision with small relative momentum compared to the
total momentum given to the hadronic system by the incident electron.
For the large values of momentum transfer covered in this experimer
124 125
the interaction is occurring over very short distances compared with
typical nucleon dimensions (for Q2=20 GeV2 we are probing distances
of approximately l/20 of a nucleon diameter). Thus a very small
fraction of the total volume of the proton is "hit." In a simple
picture, the large momentum transfer must be absorbed by a small part
of the nucleon. Nevertheless in the threshold region the whole nucleon
and any other particles produced must share this momentum in order to
recoil in a state of small mass. The cross section is therefore sup-
pressed in this region.
Elastic scattering is the extreme case: a single recoiling par-
ticle carrying away all of the momentum transferred. If the proton is
a composite particle, it is difficult for all the parts to stay together
in high energy collisions. This is particularly true if all the momentum
transfer is to a single constituent. We therefore expect small elastic
cross sections.
The range of the interaction for inelastic scattering is also
small. The large inelastic cross sections support the thesis that the
nucleon can be described by small charged constituents rather than a
smooth charge distribution. In the simple quark model the neutron and
the proton have different quark constituents which naturally leads to
a difference in the total scattering strength of these two systems.
Electroproduction experiments have demonstrated that the two nucleons
do have different scattering strengths and this difference is largest
in the threshold region (Ref. V-2) (w<q ). One of the goals of the
the present experiment was a measurement of the N/P ratio in this
region.
This chapter proceeds as follows: Elastic scattering is discussed
first and a comparison to previous data is made. The behavior of the
Wl structure function of the proton is detailed next. The extension of
previous parameterizations of older data does not agree with the present
data and alternate solutions are studied. The chapter concludes with
the neutron to proton ratio. In the analysis only the statistical count-
ing errors are used when plotting and when fitting functions to the new
data (except where noted for elastic scattering).
ELASTIC SCATTERING
Elastic scattering from protons was measured for incident energies
of 6.5 GeV, 13.3 GeV and 19.5 GeV at a scattering angle of 60'. Some
lower Q2 elastic peaks were measured at 50' and 60' with incident ener-
gies ranging from 1.5 GeV to 4.5 GeV during the experimental "check out"
periods.
These low Q2 elastic peaks are high statistics runs and clearly
show the elastic radiative tail between the proton mass and one pion
threshold. Empty target contributions were measured for each point and
subtracted from the data. An unfolding technique was employed (Ref. V-3) ^
to account for the radiation processes. Of the higher QL data only the
measurement made at Eo=6.5 GeV had sufficient statistical accuracy to
allow use of the unfolding methods.
The measured data for the two highest Q2 points are shown in
127 126
Fig. V-l. Also shown in this figure are the measured empty target
contributions. The empty target cross sections were measured to be
"flat" in the elastic peak region and all the empty target data for
Wc1.075 GeV were combined to reduce the error introduced by this
correction. 8
The radiative corrections were made using the formula given by
Tsai (Ref. V-4). An energy resolution equal to the missing energy
between the elastic peak and one pion threshold, AE'=E'(elastic)-E'(M+Mm)
was used. The final values of elastic scattering cross sections are
given in Table V-l.
6
The elastic cross section can be written in terms of the two form
factors GE and GM as
(5.2) au = - uNS (G~~+TG~~ f 2-r tan2012 GM') an 1+ =
2 uNS =Cl
4E 2 -0 sin4012 cos20/2 1 ; and T= Q2/4M2
1+2E,(sin 2- 0/2)/M
At high Q2 and large scattering angles the GM contribution to the
cross section dominates. The assumption of form factor scaling, i.e.
G =G /u E M p' is often made although there is some indication that GE falls
faster than this (Ref. V-5). Form factor scaling predicts that by a
Q2 of 5 GeV 2 and 6=60°, GE contributes only 3.3% to the cross section.
Thus, measurements at large angles are insensitive to GE, if GE is not
S2 larger than predicted by form factor scaling. GM is given in Table V-l
along with the measured cross sections, where G s2 M is defined by
(5.3) do -= dCl
uNS (G:)~ (11 p2 + T + 2T tan2e/2) l+T
IO
0.8
0.4
0
l Full Target Data o Emty Target Data (MT) I I I I I I I I
Eo= 13.3 GeV 8=60°
E’ = 1.645 GeV Q2= 21.88 GeV2
$+I) = 0.179+0.048x iO-4
- ~(MT)=0.057+0.0lI XIO-4
Ea= 19.5 GeV 6=60”
E’ = I.712 GeV Q2 = 33.38 GeV2
-0.08 -0.04 0 0.04 0.08 MISSING ENERGY CGA’)
FIG. V - 1
The measured elastic peak cross sections qff hydroge and the empt target cross sections for Q = 21.8 GeV 9
and 33.4 GeV 3 .
29
128
'Z-A '%Td UT aU?T PJTOS E SE PaJJoTd
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TS/O
.4
cm
N 0-
l al
IO
0
ts
0 0
P
I’:
rk
40
-I P
P
ti
07 1
c7
cn
-a
m
it+
is
Z 1
COUN
TS I
O.2
cm
CO
UNTS
/O.3
3 m
rad
P
TRIA
LS/O
.1
%
TRIA
LS/l
mra
d
TRIA
LS/O
.25
mra
d
LOZ 9oz
(zsoo.- > 9 > ~900’- SBM p 30 a9uel 32)
pot
(GeV
)
Xi (
cm)
3 r-
L -. -.
-+
1 3
P L -.
0
